What is the frequency of pure round seeded pea plants in `F_(2)` generation of a dihybrid cross -

Options

A. `4//16`
B. `6//16`
C. `1//16`
D. `2//16`

Answer

To find the frequency of pure round seeded pea plants in the F2 generation of a dihybrid cross, we can follow these steps:

### Step 1: Understand the Dihybrid Cross
A dihybrid cross involves two traits, each represented by two alleles. In this case, we are considering:
- Seed shape: Round (R) is dominant over wrinkled (r).
- Seed color: Yellow (Y) is dominant over green (y).

### Step 2: Identify the Parental Generation
We start with two purebred plants:
- One plant with yellow round seeds (YYRR).
- One plant with green wrinkled seeds (yyrr).

### Step 3: Determine the Gametes
From the parental generation:
- The yellow round plant (YYRR) can produce gametes: YR.
- The green wrinkled plant (yyrr) can produce gametes: yr.

### Step 4: F1 Generation
When we cross these two plants, all offspring in the F1 generation will be heterozygous for both traits:
- Genotype: YyRr
- Phenotype: All will be yellow and round since both traits are dominant.

### Step 5: F2 Generation
To find the F2 generation, we perform a self-cross of the F1 generation (YyRr x YyRr). We can use a Punnett square to visualize this.

### Step 6: Construct the Punnett Square
The gametes from each parent (YyRr) will be:
- YR, Yr, yR, yr (from one parent)
- YR, Yr, yR, yr (from the other parent)

Constructing the Punnett square gives us 16 squares, representing all possible combinations of the alleles.

### Step 7: Count the Genotypes
From the Punnett square, we can identify the genotypes:
1. YYRR (pure yellow round)
2. YYRr (yellow round)
3. YyRR (yellow round)
4. YyRr (yellow round)
5. YYrr (pure yellow wrinkled)
6. Yyrr (yellow wrinkled)
7. yyRR (pure green round)
8. yyRr (green round)
9. yyrr (pure green wrinkled)

### Step 8: Identify Pure Round Seeded Plants
The pure round seeded plants will have the genotype:
- YYRR (1)
- YyRR (2)
- yyRR (1)

Thus, the pure round seeded plants are YYRR and yyRR, which are 3 in total.

### Step 9: Calculate the Frequency
The total number of plants in the F2 generation is 16. The frequency of pure round seeded plants is:
\[ \text{Frequency} = \frac{\text{Number of pure round seeded plants}}{\text{Total number of plants}} = \frac{3}{16} \]

### Conclusion
The frequency of pure round seeded pea plants in the F2 generation of a dihybrid cross is \( \frac{3}{16} \).

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